I ran again this morning, as planned, and earlier than last time. The run started off as a bit of a struggle, but after a while it went okay, and I managed to finish the 30 minutes, running 31,5 minutes total, about 4K. I ran my old route again, and my times were:
1km 6,5 min
2km 8,5 min (total 15)
3km 8,0 min (total 23)
4km 8,0 min (total 31)

So that’s 7,7 km/hour, not too bad. More importantly: another 30min run done. :)